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 Global maps of monthly self-calibrating Palmer Drought Severity Index (scPDSI) have been calculated for the period 1901–2009 based on the CRU TS 3.10.01 data sets. This work addresses some concerns with regard to monitoring of global drought conditions using the traditional Palmer Drought Severity Index. First, the scPDSI has a similar range of variability in diverse climates making it a more suitable metric for comparing the relative availability of moisture in different regions. Second, the more physically based Penman-Monteith parameterization for potential evapotranspiration is used, calculated using the actual vegetation cover rather than a reference crop. Third, seasonal snowpack dynamics are considered in the water balance model. The leading mode of variability in the new data set represents a trend towards drying conditions in some parts of the globe between 1950 and 1985 but accounts for less than 9% of the total variability. Increasing temperature and potential evapotranspiration explain part of the drying trend. However, local trends in most of the drying regions are not significant. Previously published evidence of unusually strong or widespread drying is not supported by the evidence in this work. A fundamental aspect of the calculation of scPDSI is the selection of a calibration period. When this period does not include the most recent part of the record, trends towards more extreme conditions are amplified. It is shown that this is the principal reason for different published interpretations of the scale of recent global drying and not, as recently claimed, the use of simplified forcing data.
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 The Palmer Drought Severity Index (PDSI) [Palmer, 1965] is a measure of soil moisture availability that has been used extensively to study droughts and wet spells in the contiguous USA and elsewhere, particularly as the primary indicator of the severity and extent of recent droughts [Heim, 2002; Briffa et al., 1994; van der Schrier et al., 2006, 2006; Dai et al., 1998, 2004; Dai, 2011]. Recently, the PDSI has become more popular as a drought metric in studies quantifying possible trends in future soil moisture availability [Dai, 2011; Burke and Brown, 2006] and it has been used as the basis for reconstructing past variations in drought [Cook and Woodhouse, 2004].
 The computation of the PDSI involves a classification of relative soil moisture conditions within 11 categories as defined by Palmer  (Table 1), which range from −4 (extremely dry) to +4 (extremely wet). The index is based on water supply and demand which is calculated using a rather complex water‒budget system involving local soil characteristics and historical records of precipitation and potential evapotranspiration.
Table 1. Classification of Dry and Wet Conditions as Defined by Palmer  for the PDSI
3.0 : 4.0
2.0 : 3.0
1.0 : 2.0
0.5 : 1.0
incipient wet spell
−0.5 : 0.5
−0.5 : −1.0
incipient dry spell
−1.0 : −2.0
−2.0 : −3.0
−3.0 : −4.0
 The 2007 IPCC AR4 report [Trenberth et al., 2007] discussed a trend towards drier conditions over the 1901–2002 period, which was reported in a global PDSI data set [Dai and Trenberth, 2004]. In that study it was argued that since the middle 20th century, global aridity and the extent of areas suffering drought have increased substantially. Next to natural variability, which is a dominant factor in the occurrence and extents of droughts, such as those associated with the ENSO system, an increased atmospheric demand for moisture was identified as the critical factor in this trend.
 In the same IPCC report, and in a subsequent IPCC report on climate extremes [Seneviratne et al., 2012], the ability of the PDSI to represent soil moisture conditions was criticized for a variety of reasons. The aim of this study is to present a new global self-calibrating PDSI (scPDSI) data set, spanning the period from 1901 to 2009, which goes some way to account for the deficiencies identified in the 2007 IPCC AR4 report [Trenberth et al., 2007]. This new data set is further analyzed to test the robustness of the conclusions stated in the 2007 IPCC report and to identify the principal causes of the differences with earlier published PDSI data sets.
 The use of the Thornthwaite parameterization for Potential EvapoTranspiration (PET) rather than the more physically realistic (and complex) Penman-Monteith approach was one problem identified in the IPPC AR4 report. The parameterization for PET used here is the Penman-Monteith equation applied to the actual vegetation cover, rather than a reference crop (as is done implicitly in the Thornthwaite‒based method). The use of the more physically based Penman-Monteith estimate tests the impact of climate change on the Thornthwaite‒based estimates of PET since the latter are only based on temperature rather than (principally) on radiation.
 Another problem relates to the use of the same set of PDSI calibration coefficients that Wayne Palmer used in the 1960s when the index was proposed, regardless of the climate in the region for which the PDSI was calculated. Due to a lack of computational resources, Palmer calculated a set of empirical weighting factors by averaging results from only a few locations, mainly in the American mid‒west. These fixed weighting factors subsequently became a constant part of the PDSI computation, despite applications of the PDSI outside the American mid‒west [Wells and Goddard, 2004]. This problem is sufficiently problematic to mean that the PDSI is not strictly comparable between diverse climatological regions, and produces values which are ≥4 or ≤−4 up to 15% or more of the time [Wells and Goddard, 2004]: hardly corresponding to the statistical classification “extreme”. The self-calibrating scPDSI as proposed by Wells and Goddard  calibrates the PDSI with data which are uniquely appropriate to each location and produces a drought index which is comparable between diverse climatological regions.
 In addition to these two concerns, another handicap of the PDSI is its inability to deal with snow; it assumes all precipitation to be in the liquid phase. The lack of snowpack dynamics in the water balance calculations which are at the heart of the PDSI results in an overestimation of the availability of moisture for snowy regions in winter when the snowpack forms and underestimation when the snowpack melts. A simple snow melt and accumulation process is added to the water balance model here to account for this.
 Despite the addition of simple snow dynamics, the water balance model remains a somewhat over‒simplification [Karl, 1986]. Initiatives to deal with this shortcoming have been proposed by, e.g., Pereira and Rosa . However, in the current study we refrain from replacing the water balance model with a more realistic model, principally because the meteorological input data are monthly aggregates which hampers a more sophisticated approach to soil moisture modelling.
 Some of the modifications to the scPDSI employed in this study have been introduced earlier. The use of Penman-Monteith parameterization for PET (albeit using the reference crop rather than the actual vegetation) in studies of global changes in PDSI has been implemented in the recent work of Dai [2011, b]. The use of the self-calibrating PDSI on a global scale has also been explored previously by Dai . The inclusion of snow parameterization in the water balance calculations for the PDSI has been used before on a regional scale [van der Schrier and Efthymiadis, 2007], and a snow model developed specifically for the Canadian prairies [McKay, 1963] is actually implemented for operational PDSI estimates at the Agriculture and Agri‒Food Canada Web pages. The new aspect of the current study is the combination of all these features with the use of the newly released CRU TS 3.10.01 data set, which is based on an updated set of station data with stronger quality control than in previous versions.
 The remainder of this study is organized as follows: Section 2 describes the data sets used to calculate the scPDSI. Section 3 describes the development of the data set including a brief discussion of some issues and limitations of the scPDSI, the implementation and validation of the Penman-Monteith parameterization for Potential Evapotranspiration and the snowpack model. Section 4 presents an analysis of inferred global aridity changes based on the scPDSI data set. Section 5 compares the scPDSI data set with existing PDSI data sets and the study is summarized and results are discussed in Section 6. More technical information about the Penman-Monteith parameterization and the snow accumulation and melt model is provided in the Appendix.
2 Input Data Sets
2.1 Meteorological Data
 Gridded precipitation, temperature, cloud cover and vapor pressure data (0.5°×0.5° resolution) are taken from the monthly data set compiled by the Climatic Research Unit. This data set, designated CRU TS 3.10.01, currently spans the period January 1901 to December 2009. These data are supplemented with a gridded data set (0.5°×0.5° resolution) with climatological values (1961–1990) of monthly averages of the 10 m wind speed, which was also produced at the Climatic Research Unit. The number of records for wind which are sufficiently long to produce a data set that matches the time span of the other elements is just too low to allow the construction of anything but a climatology.
 Station records used in the construction of the gridded data have been quality controlled and checked for inhomogeneities and adjusted where necessary [Mitchell and Jones, 2005]. Precipitation and temperature were interpolated directly from station observations. Cloud cover and vapor pressure were interpolated from merged data sets comprising station observations. In regions or times where there were no station data, synthetic data were estimated using predictive relationships with the primary variables—temperature, precipitation and diurnal temperature range [New and Hulme, 2000]. For the CRU TS data sets, anomalies with respect to the 1961–1990 normal are gridded [Mitchell and Jones, 2005]. Using anomalies preserves the variance better than interpolation of absolute values [New and Hulme, 2000]. Anomalies are spatially very homogeneous and these are added to the climatological fields of temperature and precipitation which have a detailed spatial structure. The consequence of this is that in areas or times with fewer station data, the estimate of the absolute value will be close to climatology. For temperature, the station density is sufficiently high for this effect to be small. The use of predictive relationships means that for cloud cover and vapor pressure, gridded values will not be exactly equal to climatological values for the periods or areas where station data for these elements are absent.
Harris and Jones  compare the CRU TS 3.10.01 data to alternative data sets. For precipitation, this is the version 5 of the Global Precipitation Climatology Centre (GPCC) data set which spans the period 1901–2009. This data set uses considerably more stations than CRU TS 3.10.01. Analyzing trends and correlations of averaged precipitation over the regions defined by Giorgi and Francisco  shows overall high correlations, with only four regions below 0.84 (Alaska, Central America, Amazon and Southern Asia). Regions with lower correlations show greatest differences in the early years, especially before the 1930s, or in the last 10 to 20 years. Precipitation trend differences over the 1901–2009 period are large for Central America, the Amazon basin, Central Asia and Southern Asia. The regions Alaska, Central America, Southern Africa and the whole of Asia have trends over the 1950–2009 period that differ most from those in the GPCC data.
2.2 Vegetation Data
 The satellite-based Global Land Cover Characteristics (GLCC) data set developed by the U.S. Geological Survey, the University of Nebraska‒Lincoln and the European Commission's Joint Research Centre was used to characterize vegetation cover. It has a 1 km spatial resolution and is based on advanced very high resolution radiometer (AVHRR) reflectance data spanning April 1992 through March 1993.
 From this collection, we take the Biosphere‒Atmosphere Transfer Scheme (BATS) Legend. The land cover classes included in this data set are shown in Table 2. Data were regridded to the regular grid used by the CRU by using the most abundant vegetation type for each gridbox.
Table 2. Types of Vegetation Used in the Biosphere‒Atmosphere Transfer Scheme Legenda
Albedo values are from Oke [1978, Table 1.1] and VIC. Other parameter values are from ECMWF [2007, Tables 7.1 and 10.4]. The zero‒line displacement for vegetation type desert, semi‒desert and ice‒caps is set to zero since for extremely sparsely placed roughness elements, the ground surface is the true reference and d should be very close to zero [Brutsaert, 1982].
Crops Mixed Farming
Evergreen Needleleaf Trees
Deciduous Needleleaf Trees
Deciduous Broadleaf Trees
Evergreen Broadleaf Trees
Ice Caps and Glaciers
Bogs and Marshes
Water and Land Mixtures
 Information about the characteristics of the vegetation types was gathered from several sources. The typical albedo of each vegetation type was obtained from Oke [1978, Table 1.1]. Other parameters of the BATS vegetation types, like the minimum canopy resistance rs, the Leaf Area Index LAI, vegetation coverage vveg and a coefficient gD for the dependence of the canopy resistance rson the vapor pressure deficit, were obtained from the documentation for the numerical weather prediction suite IFS (Integrated Forecasting System ECMWF [2007, Table 7.1]). A summary of the parameters used and their corresponding values is given in Table 2.
 The classical Penman-Monteith equation for 24 h calculation of Potential Evapotranspiration, equation ((4)), requires the ratio between the canopy resistance rs and the aerodynamic resistance ra. The latter quantity determines the rate of water vapor transfer away from the ground by turbulent transfer. The formula for the aerodynamic resistance is
Table 3. Symbols, Explanations and Units for the Elements Used in Equations ((3)) and ((4))
latent heat flux density of evaporation
MJ m−2 d−1
net radiation flux density at surface
MJ m−2 d−1
soil heat flux density
MJ m−2 d−1
specific heat moist air = 1013
kJ kg−1 °C−1
vapor pressure deficit
bulk surface resistance of the vegetation canopy and soils
slope of the saturation vapor pressure curve
latent heat of vaporization
constant for conversion from kJ s−1 to MJ d−1
height of wind speed measurement
height of temperature and humidity measurements
von Karmann constant = 0.41
wind speed measurements at height zm
zero plane displacement of wind profile
roughness parameter for momentum
roughness parameter for heat and water vapor
ECMWF  provides values for the roughness lengths zom and zoh which are used in this study.
 The CRU wind data represent measurements at 10 m height above the vegetation (canopy) and the temperature and humidity data are representative of a height of 1.5 m above the vegetation (canopy). Using the ECMWF estimates of the zero‒plane displacement for the various vegetation types, the simple relationship between the mean height of the crop hc and the zero‒plane displacement d is given by [Shuttleworth, 1992]:
2.3 Potential Soil Moisture Storage Capacity Data Set
 The potential soil moisture storage capacity data set is taken from the Food and Agriculture Organization digital soil map of the world (FAO, 2003). The water holding capacity of the soils is subdivided in nine classes, from wetlands (which are given a water holding capacity of 1000 mm) to soils with a water holding capacity of < 20 mm. Gridboxes dominated by surface water or glaciers were excluded from the scPDSI computations. The data are regridded from 5' to 0.5 ° resolution by taking the water holding capacity of the most dominant soil type in the aggregated grid boxes so that the grid of the water holding capacity of the soils coincides with the grids of the temperature and precipitation data.
3 Developing the Global scPDSI Data Set
3.1 Potential Evapotranspiration
 Potential evapotranspiration is generally thought to be more realistically estimated using Penman-type approaches rather than Thorntwhaite‒based methods, which rely only on temperature data and latitude. However, Dai  and van der Schrier and Jones  compared scPDSI or PDSI estimates based on these two approaches and found that scPDSI values based on either of the two PET‒estimates are very similar, in terms of correlation, regional averages, trends, and in terms of classifying extremely dry or wet months. This is despite the fact that the estimates of the Thornthwaite and the Penman-Monteith parameterizations have very different amplitudes. The reason for this insensitivity relates to the calculations in the simple water balance model at the core of the scPDSI algorithm. It has been shown that in many areas actual evapotranspiration is limited by the availability of soil moisture, decoupling this quantity from its potential value. In other areas, the water balance does change, but the quantity central to the calculation of the scPDSI is, by construction, a reflection of the actual precipitation, making it largely insensitive to the choice of PET parameterization [Dai, 2011; van der Schrier and Jones, 2011].
 Notwithstanding this general insensitivity to the actual estimate for PET, the Penman-Monteith potential evapotranspiration is used here. This parameterization allows for a more tailored approach to including global variations in surface vegetation since it does explicitly include parameters which describe the vegetation characteristics. A comparison of trends in the scPDSI data sets based on the Penman-Monteith PET parameterizations using actual surface vegetation and using the reference crop is presented in section 4.1.
 The use of the Penman-Monteith parameterization has been criticised by de Bruin and Stricker . The reference evapotranspiration is defined for an extensive surface where it is assumed that water is not in short supply [Allen and Smith, 1994]. The conditions in many areas over the globe do not comply with this situation, and this will affect the local climate in these areas via, e.g., a shift in the surface energy balance. This will lead to increased estimates of potential evapotranspiration when using the Penman-Monteith parameterization. Areas which experience a decrease in precipitation will diverge from the ideal situation assumed for the application of Penman-Monteith and tend to increase the Penman-Monteith PET. This may produce a stronger drying trend than would be the case if the PET parametrization was based on radiation alone.
 Furthermore, the use of the Penman-Monteith parameterization comes at the cost of higher uncertainty in the observed forcing data, such as radiation, humidity and wind. The use of reanalysis data does not solve this problem given the known discontinuity issues in these and satellite-based estimates of surface radiation [Dai and Karl, 2006].
3.1.1 Comparison With Station-Based Data
 For a selection of stations in Europe, the FAO‒endorsed Penman-Monteith PET, equation ((4)), is calculated using daily data from the European Climate Assessment & Dataset (ECA&D) [Klein Tank et al., 2002]. PET values calculated from the latter data set are calculated using validated daily station data provided by the National Meteorological and Hydrological Services. The input data for PET which are available in ECA&D are daily minimum and maximum temperatures, daily averaged values for relative humidity and 10 m wind speeds and daily sunshine duration. PET values can be calculated for more than 400 meteorological stations from ECA&D in nine different European countries.
 Figure 1compares summer values of PET for a few stations with the corresponding gridbox values from the CRU data set. These plots indicate that the estimates based on ECA&D data are generally somewhat higher than the corresponding estimates based on CRU data (although there are a few stations where the reverse is the case, not shown). The trends in the PET series are generally similar for the ECA&D and CRU‒based data.
 The input data for the PET calculations, as provided by ECA&D and CRU, were compared for Zaragoza (Spain) (not shown). This comparison indicated that the radiation estimates could not explain the bias in the two estimates for the PET. The difference between CRU data and ECA&D data for temperature is approximately 10% (CRU being lower for both daily maximum and minimum temperatures). For wind, the difference is near 50% (CRU being lower). For vapor pressure, it is approximately 50% (CRU being higher). Modifying the ECA&D data with these percentages and recalculating PET values show that the difference in vapor pressures is the dominant contributor to the difference in PET values, especially in the earlier part of the record.
 Overall, this comparison suggests that the CRU‒based PET estimate may underestimate the amplitude of the PET, although the trends are generally similar.
3.1.2 Global Vegetation Cover and its Effect on Penman-Monteith PET
 The top panels of Figures 2and 3show the difference in the seasonal mean values of PET (mm/month) for the Penman-Monteith parametrization using actual vegetation types and the same parameterization using the reference crop. These figures show that in the African Sahel region and in southern Africa, the parameterization with the reference crop underestimates PET, whereas in general the reference crop‒based PET overestimates the PET based on actual vegetation. The strongest overestimation is in the Amazon basin where differences up to 80 mm/month are found.
 The lower panels of Figures 2and 3show the standard deviation for this difference. These show that in boreal summer (JJA) the temporal behaviour of the two PET estimates deviates most strongly in parts of Northern America, Scandinavia, eastern Europe, western Asia and parts of Australia. In boreal winter (DJF), high values of the standard deviation are found in south central North America, equatorial South America and parts of Australia.
 There is some difference in amplitude between the boreal summer and winter, but the patterns are very similar.
3.2 A Simple Model for Snow Melt and Accumulation
 In this study, the mass balance of the snow cover is estimated by parameterizing snow melt and snow accumulation. The climatic input to these parameterizations are monthly averages of daily averaged surface temperature and monthly accumulated precipitation. The proposed model represents probably the simplest possible approach that can be used and is based on a positive degree day model [Reeh, 1989; Braithwaite and Zhang, 2000; Jóhannesson and Sigurdsson, 1995]. It has earlier been used in studying moisture variability in the European Alpine region [van der Schrier and Efthymiadis, 2007]. There are several parameters in this approach, two of which, the degree‒day factor β and the standard deviation of daily temperatures σ, are calculated by tuning the snow mass balance model to satellite observations. Other parameters were empirically derived but taken from the literature. The parameters β and σ are assumed to have an annual cycle. The detailed formulation of the model, the estimation of β and σ and some validation of the accuracy of the seasonal cycle and the year‒to‒year variability are given in Appendix B.
 Here we compare GRACE Water Thickness Equivalent (WTE) anomalies, a measure of the seasonal dynamics of terrestrial water storage, with the output from the water balance model used in the scPDSI calculations. The Gravity Recovery and Climate Experiment (GRACE) satellites measure the temporal variations in the gravity field of the Earth, that can be used to retrieve changes in terrestrial water storage [Landerer and Swenson, 2012]. Figure 4shows the correlation between monthly GRACE WTE anomalies and the combined soil moisture data from the PDSI water balance model and the SWE from the snow model over the period 2000‒2009. Large and positive correlations occur over western Europe, Scandinavia, northeastern Russia, northern Asia and Canada. In some regions, such as Scandinavia and northeastern Canada, the correlations reach 0.8.
 Based on these results and those shown in Appendix B, the addition of this simple model representing accumulation and snow melt improves the realism of the water balance calculations on which the PDSI values are based.
 A comparison between GRACE WTE and global PDSI values by Dai  showed positive correlations between PDSI and the satellite data of 0.4 ‒ 0.8. Areas with low correlations coincide with arid areas where human withdrawal of groundwater may have affected the GRACE data whereas the PDSI is insensitive to this disturbance [Dai, 2011].
 A comparison of trends in the scPDSI datasets with and without the snow parameterization is presented in Section 4.1.
3.3 The self-calibrating PDSI
 The self-calibrating PDSI (scPDSI) as devised by Wells and Goddard  is a more appropriate form of drought metric for compiling a global dataset than the more common Palmer Drought Severity Index (PDSI). Where Palmer used weighting and calibration factors in his algorithm, empirically derived from a limited amount of data exclusively drawn from the US Great Plains, the scPDSI determines specific factors for each location separately, uniquely appropriate to that location, and producing fields of data that can be more validly intercompared [Wells and Goddard, 2004; van der Schrier and Briffa, 2006].
 Palmer specifically designed the index to treat the drought problem in semiarid and dry subhumid climates and cautioned that extrapolation beyond these conditions might lead to unrealistic results [Palmer, 1965, p.50]. He also stated that some regions are so near to being a desert that there is really little point in attempting drought analysis in such situations. The latter point is equally relevant to the scPDSI and it is for this reason that we do not calculate values in situations where the accumulated precipitation (over the 1901‒2009 period) is less than 5000 mm, mainly the Sahara region, parts of the Arabian Peninsula, part of northern China and parts of Chile. See van der Schrier and Jones  for a more thorough discussion of this issue.
 In the PDSI algorithm, the‘Climatically Appropriate Conditions For Existing Conditions’ (CAFEC) precipitation is calculated. The difference between the actual and CAFEC precipitation is central to the PDSI and requires the use of a base period to determine representative climatic conditions and the calculation of .
 Next to the base period, a calibration period is required for another critical step in the process which aims to make the PDSI comparable between diverse climatological regions. In this study, as well as in other studies available, the base period and the calibration period are taken as the same. In the following we discuss issues related to the choice of the calibration period.
 In order to have the probability distribution of the scPDSI roughly between ‒4 and +4, a scaling is used in the scPDSI algorithm. This scaling is based on the historical record of climate variability at each location. Changing the length of the calibration interval over which the scaling factors are calculated will change the values of the index [Wells et al., 2004, their Sect. 3a]. One motivation for using the entire historical record, from Jan. 1901 to Dec. 2009, as the calibration period in this study is that the most severe droughts and pluvials should ideally be contained within the calibration period in order to relate these events to the most extreme PDSI values and the classification‘extremely dry’ or‘extremely wet’. Using a calibration period that does not contain the most extreme data may result in index values that lie far beyond the ‒4/+4 theoretical range during periods outside the calibration interval.
 However, using the full span of climate data will mean that some early data, in the first few decades of the 20thcentury, will be of poor quality for some areas in the world, and/or data from the last few decades, reflecting possible climate change, are also included in the calibration period. This is especially worrying for the calculation of the CAFEC precipitation. It will also tend to make trends less easily detectable. Note that the use of the complete historic record as the calibration period does not imply that it is taken to be a stationary baseline. The climate record is clearly non‒stationary and contains a human‒induced warming trend that is not part of the natural variability. Further discussion on the impact of choosing the calibration period is included in section 5.1.2.
 The scPDSI should show a strong relationship with other observed measures of drought such as river discharge and soil moisture. Dai  shows that the correlations between scPDSI and streamflow of selected rivers and soil moisture time series is indeed strong. Here we compare the scPDSI with a multi‒satellite surface based soil moisture dataset covering the period 1979‒2010 [Dorigo and de Jeu, 2012; Liu and Dorigo, 2012]. Figure 5shows this correlation for the four seasons over the timespan 1979‒2009 for those areas with satellite coverage. This figure shows that the scPDSI generally correlates well with the satellite observed soil moisture, with correlations up to 0.8, especially in spring. There are some regions with negative correlations, such as the Sahel (south of the Sahara desert). Soil moisture data generated internally in the water balance model of the scPDSI algorithm correlate positively with the satellite observed soil moisture with the strongest relationship in autumn. Our interpretation of these results is that the water balance model in the scPDSI algorithm produces results which are generally realistic, despite its inherent simplifications, but the scPDSI may be less appropriate as a drought metric for this arid region [Palmer, 1965, p.50].
 A strong correlation is also found between the scPDSI data and soil moisture as simulated by the GLDAS NOAH‒2 land surface model. A simple correlation analysis of summer scPDSI values and NOAH summer soil moisture data shows correlations in excess of 0.8 over most parts of the globe. Areas where the correlation is low, or where correlations are statistically insignificant (p>0.1) include northern Canada, the central Amazon rain forest and some desert areas (Figure 6).
4 Analysis of Global Aridity Changes From 1901 to 2009
4.1 Dominant Modes of Variability and Trends
 Figure 7 shows the spatial pattern and the associated temporal evolution of the first Empirical Orthogonal Function (EOF) of the annually averaged scPDSI data. The first EOF explains a meagre 8.2% of the total dataset variance (where the second to fourth EOFs explain 6.6%, 5.7% and 4.1% respectively). The first EOF does capture a trend in the annually averaged scPDSI, showing areas with enhanced drying in Africa (with the largest signal between the equator and the Sahara desert), the Arabian Peninsula and the Middle East. This analysis also indicates drying in Alaska, Canada and Siberia north of 60 °N. However, trends in these northern regions with sparse meteorological observations should be interpreted with caution. Other areas with a less strong trend towards drier conditions are the Mediterranean and central Europe, large parts of Asia, southern South America and to a lesser extent, areas in South America between the equator and 30 °S.
 Areas that are shown to be getting wetter are large parts of North America, South America near 30 °S, Iceland, Scandinavia, eastern Europe, Australia and some isolated parts of Asia.
 The EOF analysis does not give any information on the statistical significance of the trend captured in the first EOF. The low amount of variance explained by the first EOF and the weak separation between the first and second EOFs suggest that the drying signal is difficult to distinguish from internal variability. A trend analysis using a standard linear least squares technique (NAG's e02adf) combined with an estimate of the statistical significance [von Storch and Zwiers, 1999, §8.31999] indicates that very few isolated gridboxes produce trends whose significance exceeds the 95% confidence level. The significance calculations include an estimate of an adjusted number for the degrees of freedom [von Storch and Zwiers, 1999, §6.6.7 ‒ 6.6.8] to account for temporal autocorrelation in the data. If this latter adjustment for the autocorrelation of the data is removed, then larger areas do exceed the 95% significance level and drying is observed in the circum‒Mediterranean, in Africa south of the Sahara, eastern Russia and Southwest Australia.
 In order to assess the effect of including the actual vegetation cover in the Penman-Monteith parameterization for PET on trends in the scPDSI, a trend analysis using the linear least squares method (excluding any significance testing) for 1951‒2009 was undertaken on each grid square series of scPDSI and an alternative analysis of the scPDSI data calculated using the PET estimates for the reference crop. Figure 8a shows the differences in these trends (in PDSI units/decade). The effects are modest over the largest part of the globe with some patchy areas showing a larger response. The areas which have a stronger trend towards drying when the PET estimate based on the actual vegetation is used, are parts of Canada, South America, Africa, parts of Europe and parts of Asia. The areas which have a positive trend in scPDSI are located in northern Russia and northern Siberia. Note that very few isolated gridboxes produce trends which pass the 95% confidence level.
 The effects of including a parameterization for the snow pack has effects (not surprisingly) in the higher latitudes such as northern North America, Scandinavia, eastern Europe and Siberia, and at higher altitudes like the European Alpine region, the Rocky Mountains and Himalaya (figure 8b). Again, the effects are modest over the largest part of the globe with some patchy areas showing a larger response.
 In an effort to quantify the influence of a possible temperature‒driven increase in potential evapotranspiration on the scPDSI, we calculated alternative scPDSI data using fixed monthly climatological values of the potential evapotranspiration (based on the 1961‒1990 climatology) and substituted these for the actual values in the water balance calculations. Similarly, fixed climatological temperature data needed to drive the snow model were also used. The precipitation data were not altered. In the following, the scPDSI values based on actual values for PET and the climatological values for PET are compared.
 Figure 9 shows that for the area north of 30 °N, the area percentage experiencing extremely dry summer conditions (scPDSI ≤ ‒4) varies around 2% from the 1950s to the 1990s with an increase to substantially higher values in several years of the last decade. The high values since the year 2000 are not, however, unprecedented in the period since 1901.
 Figure 9 also shows that the increase in evaporative demand has contributed to the strong increase in the size of the area with extremely dry conditions; replacing the PET values with climatological values gives an area percentage which is more within the range of prior interannual variability. For the southernmost area the increase in evaporative demand resulted in an increase in area percentage with extreme drought that is not unprecedented since 1901.
 Figure 10 shows the difference in scPDSI values calculated using actual and climatological PET and temperature, for the boreal summer of 2008 and averages over the period 2001‒2009. These summers are those shown in Figure 9to have the largest difference in the percentage of extremely dry areas. Figure 10shows that the scPDSI values based on actual values of PET and temperature indicate much drier conditions in northeastern Canada, Alaska, parts of of northern Asia and Scandinavia and parts of Central Asia.
 The area percentage showing extremely wet conditions is shown in Figure 11. This figure does not show much difference between the area percentages as calculated using scPDSI data based on actual or climatological PET and temperatures, with the exception of the area north of 30 °N and only for the last few years. However, the area percentages with extremely wet conditions are well within the variability of the time series.
4.2 Regional Changes in Dry and Wet Areas
 Figure 12 shows the percentage areas with moderately (grey) and extremely (black) dry or wet conditions defined for the regions defined by Giorgi and Francisco . The upper parts of the panels relate to the area percentages with dry conditions; the lower parts of the panels to the wet conditions.
 There is a considerable month‒to‒month variability in the estimates of the area percentages and an inverse correlation is apparent between the area percentages for dry and wet areas, consistent with an earlier analysis based on PDSI data by Dai .
 In data‒poor areas the variance of the precipitation in the CRU TS 3.10.01 dataset is low in the first decades of the record due to the method used in constructing gridded precipitation fields [Harris and Jones, 2012]. This produces a trend in variance through time that propagates into the results shown in Figure 12for these regions. This indicates that trend results for the data poor regions are most reliable from about 1940‒1950 onwards.
 Areas with a 1951‒2009 trend toward more expansive wetter conditions are seen in Central and Eastern North America. Areas where the percentage area with wet conditions shrink are the Mediterranean, Eastern Asia, Western Africa and Eastern Africa. The latter three areas display trends with a statistical significance exceeding 95%.
 On the other hand, Western, Central and Eastern North America, Central America and the Amazon Basin show a decrease in the area with relatively dry conditions but not to an extent that is significant at the 95% level. An increase in the area percentage with moderately dry conditions is seen in the Mediterranean and Eastern Asia regions. Only the latter trend is significant at the 95% level.
 Figure 13shows annual averages of potential evapotranspiration and precipitation for the areas of Northern Europe, the Mediterranean, Western North America and Eastern Asia. It shows that trends in area averages of precipitation fail to reach the 95% significance level but for these areas, increasing trends in potential evapotranspiration are statistically significant at this level, suggesting that an increase in evaporative demand is the driver for the trend in drought.
 Figure 12shows a trend towards wetter conditions for northern Europe (not significant) and a trend towards drier conditions in the Mediterranean. The trend towards drier conditions in western Europe observed by Dai [2011, his Figure 16b] may be related to the fact that his definition of western Europe includes a sizeable part of the Giorgi and Francisco  Mediterranean region.
 The area percentages for Australia and Southern Africa show on average a much larger dry area compared to wet area, especially for the moderate category. This is an indication that the scPDSI distribution is skewed towards the dry end of the spectrum. The reason for this skewness is unknown, but it might be related to the fact that large parts of these regions have very dry climates and the PDSI may not be the most suitable drought metric for these areas [Palmer, 1965, p.501965].
5 Comparison With Other PDSI Datasets
5.1 A Comparison With the Dai (2011) scPDSI Dataset
5.1.1 Dominant Modes of Variability and Trends
 Recently, Dai  published a scPDSI dataset spanning the 1850‒2008 period with a 2.5°×2.5° resolution. These data were calibrated using the 1950‒1979 period. The inputs include the merged precipitation datasets of Dai and Fung  for the period up to 1947, from Chen and Xie for the period 1948‒1978 and GPCP data [Huffman and Adler, 2009] for the most recent period.
 To calculate the Penman-Monteith PET, the CRUTEM3 temperature dataset is used (regridded to the finer resolution of 2.5°×2.5°), and the NCEP/NCAR [Kalnay et al., 1996] reanalysis from 1948 onwards for specific humidity, pressure and wind speed. Finally, net solar radiation from the Community Land Model (CLM3) simulation [Qian and Dai, 2006] is used to estimate surface downward radiation. Prior to 1948, long‒term mean values were used as substitutes for the actual values.
 Figure 14 compares the first EOF of annually averaged scPDSI values from the current study and the Dai scPDSI dataset for the 1901‒2009 period. Only gridsquares without missing data in the Dai scPDSI dataset were used in this analysis. This figure shows very similar patterns of the first EOF for the two datasets, with drying in the Mediterranean area and central Europe and in isolated areas in Africa, Asia and Australia. The temporal patterns of the first EOF in each of these datasets match very well. The explained variance is slightly higher in our scPDSI (10.1%) than in the Dai scPDSI (8.4%).
 However, differences appear when the analysis period is shortened to 1950‒2009. Figure 15 shows the first EOFs of annually averaged scPDSI of these datasets. The spatial patterns are broadly similar though with some differences in northwestern Europe, Canada, northern Asia and South America. However, the temporal patterns are very different. The EOF1 scores for the scPDSI data calculated as described here show a strong increasing trend up until 1983 and decline thereafter while the scores for EOF1 of the Dai‒data rise consistently up until 2000 and then level off.
 Figure 16 compares the regional trends in the current scPDSI dataset with the Dai scPDSI over the period 1950‒2009. The top panels show all trends. The bottom panels show only the trends which are significant at the 95% level. Significance testing is done using the Mann‒Kendall trend‒free prewhitening procedure [Yue and Pilon, 2002]. This figure shows that very few trends suggested by the EOF1 are significant in either of the datasets.
5.1.2 The Effects of Varying the Calibration Interval
 The Dai‒scPDSI [Dai, 2011] tends to have stronger magnitudes in the trends than in the scPDSI data presented in this study. This discrepancy cannot be explained by stronger trends in the forcing data, which are very similar (not shown). Here we argue that these differences are related to the use of only a part of the historic record (1950‒1979) as the calibration interval in the [Dai, 2011] data, compared to the use of the whole of the observational record (1901‒2009) for the current scPDSI.
 The calibration in the scPDSI algorithm is based on the historical record of each location. Different calibration intervals will result in different index values [Wells et al., 2004, their Sect. 3a], which can be demonstrated by the following. The calibration aims to scale the climatic characteristic K, whose purpose it is to adjust the drought metric to the characteristics of the local climate. The traditional PDSI values are calculated first, following the original Palmer  algorithm. Based on the resulting monthly timeseries for PDSI, the 2ndand 98thpercentiles are calculated for each grid square. The climatic characteristic is then multiplied with the factor ‒4/(2nd percentile) if precipitation is lower than the reference value, or 4/(98th percentile) if precipitation is higher than the reference value, where the numbers‘‒4’ and‘4’ relate to the expected 2nd and 98thpercentiles of extreme droughts and pluvials respectively and were selected by Palmer  as threshold values for the indications‘extremely dry’ and‘extremely wet’. Based on the rescaled climatic characteristic, the self-calibrating PDSI values are re‒calculated.
 The values corresponding to the 2ndand 98thpercentiles may vary dramatically when the calibration period is changed. This is especially true if the calibration period excludes the major droughts or pluvials of the historic record, relating months with less extreme dry or wet conditions to the category‘extreme’. This effectively amplifies the index values outside the calibration period to values well outside the ‒4/+4 range. The consequence is that the interpretation of the index values, as originally envisaged by Palmer , becomes problematic since index values are reached which are much more negative or positive than the ‒4 or +4 thresholds associated with the most extreme conditions. Another consequence is that the probability distribution of the index values over the complete historic period will have a different shape than that for grid squares where a major drought or pluvial happens to fall in the calibration period. This means that the scPDSI fails to produce an index which is comparable between diverse climatological regions, invalidating its use for establishing a global perspective on relative drought.
 The amplification of index values when using the 1950‒1979 period for calibration is illustrated in Figure 17for the Giorgi and Francisco  regions Central North America and Northern Europe. Both these regions have their driest years prior to the start of the calibration period and their wettest year after the end of the calibration period. For Europe, these years are 1921 and 1981 respectively [van der Schrier and Briffa, 2006], for the contiguous USA these are 1934 and 1983 respectively [van der Schrier and Briffa, 2006]. Figure 17shows the difference in percentage area for extremely dry (PDSI ≤ ‒4) and extremely wet (PDSI ≥ 4) conditions between the scPDSI dataset using the 1950‒1979 period for calibration (similar to that used by [Dai, 2011]) and the scPDSI dataset using the complete length of the historic record (as in this study). The forcing datasets are similar for both scPDSI datasets. The curve shows steep increases in the area affected on both sides of the 1950‒1979 calibration interval which are absent when the entire length of the historic record is used as the calibration interval (Figure 12).
 The amplification of scPDSI values when the calibration interval does not span the entire historic record is also illustrated in Figure 18which shows the percentage of extremely dry months (scPDSI ≤ ‒4) for each gridbox. Figure 18a shows this quantity for the current scPDSI dataset calculated using the calibration interval spanning the entire historic record. It shows that much of the globe has a percentage near 2% when the long calibration interval is used with isolated areas where the percentage increases to approx. 5%. Figure 18b is similar to Figure 18a except that it uses scPDSI values calibrated over 1950‒1979, using the same forcing datasets. It shows that changing the calibration period produces many areas where the percentage of extremely dry months is up to 15%. Figure 18c relates to the Dai‒scPDSI values (using the same calibration interval as Figure 18b) and shows a similar pattern of patches where a high‒percentage of months indicate extremely dry conditions.
 The choice of calibration interval also affects trends in the index values. A similar comparison based on a Principal Component Analysis as in Figure 15, between the Dai‒scPDSI and the scPDSI presented in this study (the latter re‒calculated using the 1950‒1979 calibration period) shows a continued increase in the trend of the first EOF in both datasets (not shown). Note that the EOF analysis is based on the covariance matrix (rather than the correlation matrix) and so is susceptible to the high scPDSI values that occur outside the calibration interval.
5.2 Effects of Forcing and Calibration on Trends in Drought
 It has been claimed that the previously reported increase in global drought [Dai et al., 2004, Dai, 2011, Trenberth et al., 2007] is largely explained by the use of an oversimplified parameterization of potential evapotranspiration [Sheffield and Wood, 2012]. Here we show that using a calibration interval in the self-calibrating PDSI which does not extend to the end of the historic record, explains a more sizeable part of the trend towards global drought than the choice of the parameterization of potential evapotranspiration. Figure 19shows the percentage of global land area with extremely dry conditions (PDSI ≤ ‒4) calculated using three scPDSI variants. The grey bars represent the dataset presented in this paper (using the Penman-Monteith formulation and calibration interval spanning 1901‒2009). The red line shows scPDSI calculations using the simpler Thornthwaite formulation for potential evapotranspiration and again using the 1901‒2009 period for calibration. The black line shows the scPDSI calculations using the Penman-Monteith formulation but based on the 1950‒1979 calibration interval.
 This figure shows that the trend towards more widespread drying is enhanced when using the simpler Thornthwaite parameterization for potential evapotranspiration in the scPDSI when averaged over the globe, in agreement with Sheffield and Wood  (no significance testing applied). However, the effects on the trend towards more widespread drying are much greater when the 1950‒1979 calibration is used, even though the more realistic Penman-Monteith formulation for potential evapotranspiration is used.
6 Summary and Discussion
 The IPCC AR4 report [Trenberth et al., 2007] identified a widespread trend towards drier conditions since the middle 20th century based on a global PDSI dataset [Palmer, 1965; Dai and Trenberth, 2004]. However, some concern was raised regarding the realism of the PDSI algorithm and its suitability for global analyses. In this study, we present a new global dataset of monthly self-calibrating Palmer Drought Severity Index (scPDSI) with a spatial resolution of 0.5 ° spanning the period 1901‒2009.
 The scPDSI is a variant of the much more common Palmer Drought Severity Index (PDSI), but potentially represents a more appropriate index for comparing the relative spatio‒temporal variability of soil moisture changes over wide regions and hence is a more realistic and convenient metric of relative moisture supply.
 The PDSI was criticized for a number of reasons in the 2007 IPCC AR4 report [Trenberth et al., 2007]. The use of the self-calibrating PDSI variant of the‘traditional’ PDSI addresses some of these points of criticism.
 Central to the scPDSI is a simple water balance model which is driven by precipitation and Potential EvapoTranspiration (PET). In this study, the more realistic Penman-Monteith formulation for PET is used rather than the more common, and simpler, Thornthwaite parameterization. Moreover, the Penman-Monteith parameterization of PET is modified here to include the effects of the actual vegetation cover, rather than assuming a standard reference crop (short clipped grass) which is common. It is shown in this study that this modification does have a strong impact on estimates of the PET, although the effects on the actual scPDSI values are minor [Dai, 2011; van der Schrier and Jones, 2011]. Note that Alley  previously noted the unrealistic nature of assumptions in the scPDSI algorithm in relation to vegetation, related to the absence of seasonal changes in vegetation phenology and root development. This issue has not been resolved in the current study.
 The usual implementation of the (self-calibrating) PDSI assumes that all moisture is in the form of rain [Karl, 1986], which is untenable in higher latitudes or higher altitudes. Here the soil‒moisture model is modified by the addition of a simple snow‒accumulation and melt model. It is shown that the combined estimates of the snow water equivalent and the water balance derived‒soil moisture, which are at the core of the scPDSI, correlate well with GRACE satellite water thickness equivalent data (see Appendix B). It is also shown that the seasonal cycle of the snowpack is reasonably well simulated, giving a more realistic estimate of the seasonal availability of water.
 Despite the shortcomings of the original PDSI, Dai and Trenberth  showed that PDSI values are significantly correlated with measured soil moisture in the warm season. More recently, [Dai, 2011] has demonstrated a convincing relationship between scPDSI and streamflow and between scPDSI and satellite-observed liquid water thickness equivalent.
 Calculating the trends in the scPDSI over the periods 1901‒2009 or 1950‒2009 for each grid square indicates that only a few isolated grid squares exhibit trends that are statistical significant at the 95% confidence level. When a less rigorous test is applied, ignoring the autocorrelation in the scPDSI, larger areas show apparent statistically significant trends towards either wetter or drier conditions. So when taking auto‒correlation into account, there is no strong case either for very notable large‒scale moisture increase or drying in this dataset.
 A Principal Component analysis does reveal a major pattern of increasing availability of moisture across most of North America (excluding Alaska), eastern Europe, much of Argentina and Australia contrasting with drying conditions in most of central Africa, the Middle East and the Mediterranean and central Europe. However, this pattern accounts for less than 9% of the variability in scPDSI over the global land and is associated with a trend, predominantly between about 1950 and 1985 and with the strongest drying found in the Sahel region. The low amount of variance explained by the first EOF is insufficient to allow this trend to be distinguished from internal variability.
 A comparison with the recently published [Dai, 2011] scPDSI dataset shows that the dominant mode of variability in the current study and in the Dai scPDSI dataset for the 1901–2009 period are very similar, with a temporal evolution suggesting a trend toward drying. However, the same analysis for the 1950–2009 period shows an initial increase in drying in the dataset presented in this study, followed by a decrease from the mid‒1980s onwards while the Dai data show a continuing increase up to 2000. In spite of this difference, the associated spatial patterns are similar.
 A trend analysis, using a more sophisticated significance test, shows that very few local trends suggested by the most dominant mode of variability pass the 95% significance test. This is true for both datasets.
 Averaging over the regions defined by Giorgi and Francisco , we find that a trend towards more widespread drought is evident in the Mediterranean and Eastern Asia. A trend towards an increase in the area with wet conditions (and smaller area with dry conditions) is found in Western, Central and Eastern North America.
 For the Mediterranean, Northern Europe, Western North America and Eastern Asia regions, a statistically significant trend in the area‒averaged annual potential evapotranspiration is found for the 1951‒2009 period. In these regions, trends in annual precipitation are not statistically significant.
 In an effort to explain the difference in trend amplitude between the scPDSI dataset developed in this study and that of [Dai, 2011], we identified the use of a shorter calibration period in the latter study (spanning 1950‒1979) as the main cause. In a situation where the driest and/or wettest months happen to be outside the calibration period, the scPDSI algorithm amplifies the index values outside the calibration interval, while maintaining the index values in the calibration period roughly between the ‒4/+4 bounds. The consequence of this amplification is that interpretation of the index values using Palmer's classification (Table 1) is difficult and the important aspect of the scPDSI (producing an index that is comparable over diverse climatological regions) is lost.
 There is evidence, based on theory and idealized numerical experiments, that global warming will lead to an increase in the lower‒tropospheric water vapour and a slowing of the large‒scale atmospheric circulation [Held and Soden, 2006; Schneider and O'Gorman, 2010]. The poleward vapour transport and the amplitude of the pattern of evaporation minus precipitation increases proportionally to the lower‒tropospheric vapour. In this sense, wet regions get wetter and dry regions drier [Held and Soden, 2006]. This signal is not evident in the current scPDSI dataset, suggesting perhaps that climate variability on interannual and decadal timescales is too dominant at regional scales and may obscure a potential climate change signal.
 In conclusion, the evidence for unusually strong or widespread annually averaged drying, as suggested in the 2007 IPCC AR4 report [Trenberth et al., 2007] is not supported by the evidence of the current work, with the possible exception of the land areas between 30 °S and 30 °N which have seen unprecented dry conditions in the 1980s and 1990s. The scPDSI maps do show that the percentage of extreme drought (PDSI ≤ ‒4) across the Northern Hemisphere north of 30 °N has increased in the last few years but not to an extent that is unprecedented in the record since 1901. The analysis reported here suggests that part of the drying trend in the last few decades is related to increases in temperature and Potential Evapotranspiration. However, the areas most affected are still isolated (Figure 16) and no strong indication of a widespread drying trend is evident (Figure 9).
Appendix A: Calculation of the Penman-Monteith Potential Evapotranspiration
 The classical Penman-Monteith equation for daily sums of potential evapotranspiration is: [Allen et al., 1994, equation 2.1]
Explanations of all terms in ((3)) are given in Table 3.
 Equation ((3)) includes all parameters which govern the energy exchange and corresponding latent heat flux from (uniform) fields of vegetation. This is sufficiently general to represent the effects of the actual vegetation cover on the PET estimate.
 Simplifying ((3)) to represent the rate of evapotranspiration of a hypothetical reference crop with an assumed crop height of 0.12 m, a fixed surface resistance of 70 s m−1 and an albedo of 0.23 (closely resembling the evapotranspiration from an extensive surface of grass with adequate moisture supply [Allen and Smith, 1994]), the Penman-Monteith parameterization reduces to
This parameterization is referred to as the Food and Agricultural Organization (FAO) Penman-Monteith equation [Allen and Smith, 1994; Ekström and Jones, 2007]. The various inputs to this formula are explained in Table 3.
 In the absence of a dataset of monthly mean wind speed measurements from 1901 onwards, we take the gridded 1961‒1990 monthly normals for wind speed provided by the Climatic Research Unit [New and Hulme, 1999], reduced from the 10 m measurement height to 2 m using the logarithmic wind profile, and use these values as proxy values for the monthly winds. The soil heat flux for monthly values is related to monthly mean of daily averaged temperatures of the preceding and following months [Allen et al., 1994, their equation 1.57]. The slope of the vapour pressure curve, Δ, is calculated based on the saturation vapour pressure and the monthly mean of daily averaged temperatures. The net radiation at the crop surface, Rn, is calculated as the difference between short wave radiation and the long wave radiation. The first is related to monthly averages of cloud cover and monthly averages of daily total extraterrestrial radiation. The latter is based on a grey body radiation, using as input both monthly averages of daily minimum and daily maximum temperatures, effective emissivity of the atmosphere (related to relative humidity), emissivity by the vegetation and an adjustment for the cloud cover [Allen and Smith, 1994].
Appendix B: Formulation and Validation of the Snow Melt and Accumulation Model
B1 Snow Melt
 Snow melt is treated using the simple relation:
where M represents snow melt, βis the degree‒day factor (in mm water equivalent per day per °C) and Tpdd is the sum of all positive daily mean temperatures (in °C) during the period of interest. The degree‒day factor is a constant which is usually estimated from field data and varies with location and according to whether the surface consists of ice or snow [Braithwaite and Zhang, 2000]. Typical values for snow on the Weissflugjoch (Switzerland) and the Grosse Aletschgletscher (Switzerland) are 4.5 and 5.5 mm day−1 °C−1respectively.
 Here, the degree‒day sums need to be estimated from monthly mean temperature data. This can be done, assuming that the daily temperature data fluctuate around the monthly mean with a Gaussian distribution and specified standard deviation σ. The assumption of Gaussian behaviour is not strictly valid, since temperatures are slightly skewed toward high values in summer and skewed toward low values in winter, but is justified here by the requirement for simplicity of the model. This conversion is given by Reeh  and Jóhannesson and Sigurdsson . The (positive) degree‒day sum for monthly data is
where, again for the sake of simplicity, all months are assumed to be of equal length. Integration is over temperature T and Tmthe monthly mean temperature from the CRU TS 3.10.01 dataset.
B2 Snow Accumulation
 Snow accumulation at any particular altitude is estimated for each month from monthly mean temperature and monthly precipitation by assuming that precipitation is split between rain and snow according to the fraction given by equation ((B3)). The threshold where the fraction snow vs. rain equals 0.5, is typically about 1 °C [Jóhannesson and Sigurdsson, 1995]. This parameter is fixed at this value. When the temperature is specified as monthly mean values, the fraction f of the precipitation that falls as snow in a given month is given by:
where Ts is the rain/snow threshold temperature and σis the standard deviation of daily temperatures [Jóhannesson and Sigurdsson, 1995]. Again for simplicity the assumption is made that Tsis constant throughout the year.
B3 Estimation of the Parameters
 The‘free’ parameters in the above parameterizations are β and σ. These parameters are estimated using satellite-derived snow water equivalent (swe) data [Armstrong and Brodzik, 2010] obtained from NSIDC. These data span the period November 1978 to October 2006. The NSIDC data are first regridded onto the CRU 0.5°×0.5° regular grid. The period January 1979‒December 1994 is used as the calibration interval. Using a standard routine for finding a minimum in a sum of squares (NAG's e04fyf), we make estimates for β and σ for each month separately which minimise the sum of squares of the difference between observed and modelled swe. This is done for each gridbox. Months with very little snow (on average less than 2 mm swe determined over the calibration period) are assumed to be snowless and the values of σ and β are set at σ=2.5°C and β=10 mm day−1 °C−1. The latter, rather large value is chosen to ensure that if the model predicts snowfall, it will melt away very quickly.
 No estimates for βand σ are made for those gridboxes for which the accumulated snow over the complete calibration period is zero.
B4 Validation of Snow Model
 The average snow cover for November, January and March over the period Nov. 1978‒Oct. 2006 from the satellite data and the model formulated in sections B1 and B2 has been compared. Figure 20 shows the extent and snow water equivalent of the snowpack. The extent of the snow cover is generally well captured by the model. Differences between observed and modelled snow extent are most obvious in the south eastern parts of Asia and western Europe.
 The accuracy of the seasonal cycle and the year‒to‒year variability has also been investigated using area‒averaged snow water equivalent estimates based on the satellite data and the simple snow model. Figure 21shows the observed and modelled swe from 1980 to 2006 for several areas in the Northern Hemisphere.
 The authors wish to thank Aiguo Dai for stimulating discussion and three anonymous referees for their constructive comments.
 The CRU TS 3.10.01 dataset can be downloaded from the British Atmospheric Data Centre http://www.badc.rl.ac.uk/. The Global Land Cover Characteristics (GLCC) vegetation cover can be downloaded from http://edc2.usgs.gov/glcc/background.php. The Food and Agricultural Organization's soil map of the world can be accessed at: http://www.fao.org/geonetwork/srv/en/main.home. GRACE land data were processed by Sean Swenson, supported by the NASA MEaSUREs Program, and are available at http://grace.jpl.nasa.gov. Work on the scPDSI at KNMI and CRU was funded by the UK Natural Environment Research Council (NERC) through grant NE/G018863/1 and partly supported by the European Community Seventh Framework Programme (FP7/20072013) under Grant Agreement 242093 (EURO4M: European Reanalysis and Observations for Monitoring). JB was supported by a doctoral scholarship from the Chilean Government under the program Formación de Capital Humano Avanzado of CONICYT. KRB also acknowledges recent NERC support through grant NER/T/S/2002/00440/. PDJ is also supported by the US Department of Energys Office of Science, Office of Biological and Environmental Research, and the National Oceanic and Atmospheric Administrations Climate Program Office through the International ad‒hoc Detection and Attribution Group (IDAG).